This note supplements an article on ‘Organising a three-way referendum’ published on The Economist website (16th January 2019). It offers a worked example to show how the three main approaches to three-way ballots operate and some of the challenges they throw up. It reinforces Ken Arrow’s result that there is no ideal way of combining individual preferences to select one of three options.

And then, when the answer is known, to ask (say, a month later to allow time for campaigning):

Round 2: “Now you know how we would leave, would you prefer to leave or to remain?”

This ordering solves the fundamental flaw of the referendum in June 2016—that no-one knew what “leave”’ meant. It is clearly preferable to the alternative ordering which asks first whether you want to leave and then later (or at the same time) which leave option you prefer.

(2) An alternative vote, which has all three questions on the ballot and asks voters to indicate their first choice and, if they wish, a second one. If one option receives 50% of the votes, it wins. Otherwise, the question receiving the fewest first preferences is eliminated and its proponents’ second choices are distributed over the remaining options. The one that has most votes after this is the winner.

(3) A Condorcet vote, named after an eighteenth-century French philosopher, consists of a single ballot that runs three, two-way races: A vs B, B vs C and C vs A.

If we have three options on the ballot, there are six possible orderings that an individual might have. These are given in Block (I) of the table and for concreteness, each is labelled with the name of a Conservative minister whose words or actions suggest that they would adhere to that ordering. Thus, for example, John Redwood, having long opposed the EU, clearly prefers ‘no deal’ to ‘deal’; Ken Clarke, on the other hand, would like to ‘remain’ but accepts ‘deal’ as the politically responsible thing to do. Boris Johnson and Justine Greening have both declared the PM’s deal to be the worst of both worlds.

Block (II) of the table gives four entirely fictitious distributions of voters (in percent) across orderings; it is not intended to imply any judgement about actual preferences in the UK.

Distribution 2 is much more extreme, with 45 percent preferring ‘no deal’ to 10 for ‘deal’ and 45 for ‘remain’.

Distribution 3 has ‘remain’ as the favoured single option, but still with not enough preferences to beat the combined ‘leave’ positions.

Distribution 4 just shows that gaming is possible in the alternative vote. It is distribution 3 except that 5 Soubreys pretend to be Johnsons. Now ‘deal’ has fewest first preferences (30) and is eliminated and, after redistribution, ‘remain’ beats ‘no deal’ by 62 to 38. But, of course, distribution 4 could arise from genuine preferences, in which case we see that different rules for the three-way ballot imply different outcomes.

Disclaimer:The opinions expressed in this blog are those of the author alone and do not necessarily represent the opinions of the University of Sussex or UK Trade Policy Observatory.

Republishing guidelines:The UK Trade Policy Observatory believes in the free flow of information and encourages readers to cite our materials, providing due acknowledgement. For online use, this should be a link to the original resource on our website. We do not publish under a Creative Commons license. This means you CANNOT republish our articles online or in print for free.

The UKTPO exists to provide independent and objective advice on the economics and law of Brexit and trade policy. The question of whether to hold a ‘second’ referendum is essentially a political one. However, how to organise such a referendum is a technical question on which economists have something to offer.

Given the divisions in the country it seems plausible to argue that any referendum should offer three alternatives:

For example, Professor Vernon Bogdanor suggests a two-stage referendum in which we ask first whether people want to leave and then, a week or so later, what form leave should take. Professor Meg Russell, in an excellent contribution to the Today Programme today (17th December 2018; at 2.39:50) characterised this as ‘difficult’, because how you vote in the first round is influenced by your hopes or expectations of the outcome of the second.

Professor Russell is quite correct – Professor Bogdanor’s ordering replicates the fundamental problem with the first referendum: no-one would know what ‘leave’ entailed. However, if we simply reversed the order of the questions, this problem would be avoided. Hence, on the assumption that the details of each option had been properly explained, I recommend a two-round referendum with:

Round 1: ”IF we leave the EU, would you prefer ‘no deal’ or ‘Mrs May’s deal’?”

Then, when the answer to this is known (say a week later),

Round 2 asks “Now you know how we would leave, would you prefer leaving or staying?”

The decision that would face the UK public in a referendum is sequential – the step of leaving inevitably precedes the step of implementing post-leave arrangements. Economists have long understood that the way to make optimal decisions in such circumstances is through a process known as ‘backward induction’. You start with what will be the last step of the actual process (which of the forms of ‘leave’ you prefer) and work backwards to determine whether the best of the leave options is better than remaining. So, in the first step, the UK electorate determines whether it would prefer no deal to Mrs May’s deal, and then knowing what it will get from leave, whether it wants to go down that path at all.

Disclaimer:The opinions expressed in this blog are those of the author alone and do not necessarily represent the opinions of the University of Sussex or UK Trade Policy Observatory.

Republishing guidelines:The UK Trade Policy Observatory believes in the free flow of information and encourages readers to cite our materials, providing due acknowledgement. For online use, this should be a link to the original resource on our website. We do not publish under a Creative Commons license. This means you CANNOT republish our articles online or in print for free.

Alasdair Smith is an Emeritus Professor of Economics at the University of Sussex and is a member of the UK Trade Policy Observatory.

The UK Cabinet has signed off the draft EU Withdrawal Agreement (WA) and the Political Declaration (PD) about the future UK-EU trade relationship. The WA has had such a rocky reception in the Conservative Party that the future path of decision-making is a bit uncertain, but it is likely that these documents will also be agreed by the EU summit later this month. The decision-making then passes one way or another to the UK Parliament. Politics has dominated this week’s debates, but decisions need to be informed by economic assessment. Let’s consider the economic costs and benefits of the choices which Parliament will have to make.